Elementary waves, Riemann problem, Riemann invariants and new conservation laws for the pressure gradient model

Abstract

We study the pressure gradient system of nonlinear conservation laws. We present the parametrization of shocks and rarefaction waves, then the solution of Riemann problem is given. Relying on the Riemann solution, we establish the uniqueness of the Riemann problem for the pressure gradient system. We also formulate the Riemann invariants corresponding to the pressure gradient system. We will present some interesting applications for the Riemann invariants. The first application is to represent the pressure gradient model in a diagonal representation. Actually this diagonal form admits the existence of global smooth solution for the pressure gradient system. The second application is to give new conservation laws corresponding to the pressure gradient model.